QuanTek Econometrics Software

QuanTek Main Graph

One of the most important features of QuanTek
is its Main Graph, with five different scales. The
scales are labeled by the number of pixels per data point, and these
are scale 1, 2, 4, 8, 16. On each scale the entire
2048-day set of data is displayed, in multiple
views spanning the whole range, but these are views of different
sections of the same graph. The graphs show logarithmic
prices rather than actual prices, so equal intervals on the vertical
scale correspond to equal percentage changes in
value. Since the data are corrected
for splits & dividends, you can get a picture of
the true value of the security as it has evolved
over the past 2048 days (8 years). This is also the
type of data preparation needed for the Adaptive (Wavelet)
Filter to operate and make a meaningful Price
Projection.

These scrolling graphs also have the property
that you can move to any part of the graph by scrolling
and switching views. (The blue
toolbar arrows scale the graph up or down, while
the magenta toolbar arrows switch
between different views along the horizontal axis.)
When you scroll the horizontal scroll bar, the vertical scroll bar
moves automatically to keep the center line of the graph centered in
the display. You can also adjust the vertical scroll bars yourself,
if necessary. So by scrolling and switching
views, you can move to any part of the 2048-day
graph, which forms a single graph view of
the past 2048 days of corrected prices.

Note: The scale on the right shows the
prices for stocks, so long as they lie in a reasonable
range. However, if the price range is too high or
too low, or it is an index or mutual fund,
then the price scale is replaced by a symbolic scale with the
current price indicated by dollar signs. The price
for all securites at any point is also indicated by tooltips.
If you move the mouse pointer anywhere in the graph, it displays the
date and price corresponding to
that point. So you can find the price at any point in the graph just
by moving the mouse pointer to that point, no matter what the range
of the price.

Scale 4 (2019-01-04)

We begin with Scale 4, since this scale is
displayed initially when a graph opens. Here is a graph of
Amazon:

On this scale you see the 512-day (acausal)
Savitzky-Golay Smoothing Curve (yellow curve in center).
The "acausal" means that at any point, the
smoothing mixes up both past and future
data -- the smoothing is over the whole graph at once. Hence as time
progresses, the smoothing curve at past points can change. But this
means that there is also no time delay in the
smoothing curve. This smoothing curve is also projected ahead
N days, where N is the
Time Horizon setting for the calculations (here, 32
days). (The present time is denoted by
"ZERO".) So it provides yet another kind of Price Projection,
abeit a simple one.

Surrounding the S-G Smooting Curve are the
Bollinger Bands. These are spaced from the
S-G Curve by 1x and 2x
the average absolute deviation of the prices from
the 512-day S-G Smooting Curve. This is the average
trading range to be expected normally, in the absence of
any exogenous events. These curves also serve as
overbought/oversold indicators. In the above graph,
you can see that the price in September appears overbought,
ranging above its outer Bollinger Band, and then at
the end of December it undergoes the selling climax
and becomes oversold, ranging below its outer
Bollinger Band. Presumably, due to the
return to the mean mechanism, the price will tend to return
back to the central S-G Smooting Curve.

In blue on the right is the Price Projection,
due to the Default Adaptive Filter. (You can also
calculate a second filter of your choice and toggle the display back
and forth between the two for comparison.) The calculates the
expected N-day return and displays it as a straight
line, starting from the average price of the latest
trading day (average of open, high, low, close prices). This
expected return is also displayed in the header
information. The Default Aptive Filter used is a
Least-Mean Square filter, which is a
low-pass filter. Hence any features shorter in duration
than N days (in this case, 32 days)
does not have much effect on the Price Projection.
Generally, but not always, the Price Projection is
an indicator of the long-term trend. This can be
seen above since the Price Projection is
approximately parallel to the projection from the
S-G Smooting Curve. The fluctuations shorter than
N days are averaged out and only the
long-term trend remains. When presented as above, the
Price Projection is close to what the
Random Walk model would predict. (Except the Random
Walk model does not make clear how the long-term
trend is to be computed -- it takes the long-term
trend as fixed a-priori.)

The blue bars on the Price Projection are
error bars. Just as the Price Projection
represents the expected N-day return, the
error bars represent the expected N-day range
of prices. This is obtained by measuring the average
absolute deviation (1-day range or
high minus low) of the log prices, and
then multiplying this by the square root of N, for
N future days. (This is
only an estimate. There is also a direct
measurement of the average N-day range
available on the toolbar, which usually turns out to be smaller than
this estimate, so it is a conservative
estimate).

Also notice the green arrows which are Buy Points.
There are also red arrows above the graph which are Sell
Points. These correspond to the Relative Price
(band-pass) display which is a type of oscillator.
So these arrows represent N-day inflection points
in the Relative Price graph. But the Buy
Points are only shown when the Price Projection
is positive, and the Sell Points are only shown
when the Price Projection is negative. These
Buy/Sell Points are useful for swing
trading. They also depend on the setting of the
Range control in the Trading & Portfolio Parameters
dialog.

The graph along the bottom is the logarithmic volume,
relative to its average value. The bars range from the average (log)
value to a factor of 10 above and below the average value of the log
volume. (Since the logarithmic values are plotted, multiplying and
dividing the volume by 10 corresponds to the same distance above and
below the average log value.) The volume has been
extended to future values using the Standard LP
filter, mainly for aesthetic reasons. (The number in the lower right
corner is the size of the data set. However, only 2048 days are
used.)

Scale 8 (2019-01-04)

Here is the graph of Amazon on Scale 8.
Both horizontal and vertical axes are doubled in size from
Scale 4, preserving the aspect ratio. In
other works, the slope of all graphs is preserved,
enabling direct comparison of N-day returns over
any interval:

Notice how all the slopes are preserved between the two graphs.
But all the features are twice as large. You can compare the
risk of different securities by comparing the width of the
Bollinger Bands, but you must do this with all
securities on the same scale.

The main feature that distinguishes this graph is that the daily
prices are represented by candlesticks. These
display the price range from low to high
by a vertical line. The open and close
prices are represented by the upper and lower edges of the
rectangles. If the close is higher than the
open, the rectangle is light blue, and if
the close is lower than the open,
the rectangle is dark blue. This provides a way to
display the open prices, which are not displayed in
the more usual method as in Scale 4.

In Scale 4 the Buy/Sell Points
were displayed as green/red arrows. Scale 8
does not display these, but instead displays Buy/Sell
Signals as green/red rectangles. The
difference is that the Buy/Sell Signals are derived
from the Relative Price
(low-pass) display which is a type of
overbought/oversold indicator. It corresponds closely to
the price level relative to the Bollinger
Bands on the graph. There are no green/red
rectangles on this particular graph, but in other areas of
the graph they may be seen just below/above the
range of prices. This is because they indicate the optimum
buy/sell levels for GTC buy/sell orders.
The level at which these are set depends again on the Range
control in the Trading & Portfolio Parameters
dialog. Thus, despite appearances, the prices in the above graph, on
a 32-day average, are actually within a normal
trading range and hence do not trigger the
buy/sell signals. On a shorter time scale, or with a
different setting of the Range control, the
buy/sell signals might be displayed at the price extremes
of the above graph. (They can also be displayed in the
future Price Projection by means of the future
projection of the Relative Price
indicator, via the Standard LP filter.)

Scale 16 (2019-01-04)

Here is the graph of Amazon on Scale 16.
Both horizontal and vertical axes are doubled in size from
Scale 8, preserving the aspect ratio. In
other works, the slope of all graphs is preserved,
enabling direct comparison of N-day returns over
any interval:

As in Scale 8, the daily
prices are represented by candlesticks. These
display the price range from low to high
by a vertical line. The open and close
prices are represented by the upper and lower edges of the
rectangles. If the close is higher than the
open, the rectangle is light blue, and if
the close is lower than the open,
the rectangle is dark blue. This provides a way to
display the open prices, which are not displayed in
the more usual method as in Scale 4.

This graph is very big and I thought it
would be a good place to plot the actual historical Price
Projections. In other words, the Price Projection
for all days in the past is plotted on this graph for each
corresponding day. For a given day
in the past, the positive price projections are
marked by a little green rectangle at the close
price, and the negative price projections are
marked by a little red rectangle at the close
price. Then, for the N-day Price Projection, the
projected price for each given day is shown by a
double-triangle, green for a positive Price
Projection and red for a negative
Price Projection. These N-day Price Projections
for each day are called the N-day Price Target for
that day.

This can also be viewed as a representation of the Long/Short
Signals, which are just the estimated
returns from the Price Projections. The
green/red rectangles mark the days for which the Long/Short
Signals are triggered. These
are also plotted as the N-day Projected Future Returns
in one of the splitter windows. Whether these
Long/Short Signals are triggered depends on the
setting of the Threshold control in the Trading & Portfolio Parameters
dialog. So the Long/Short Signals represent intervals in which the optimal
position should be long/short, according
to the Price Projection. Note that, once again, the
expected return of the N-day Price
Projection represents an N-day smoothed optimal position. The short-term price
fluctuations in the graph do not affect the slope
of the Price Projection very much, and hence the
optimal position is also not affected very much by
these short-term price swings.

Scale 2 (2019-01-04)

Going down now in scale from Scale 4, we have a
graph of Amazon on Scale 2. Once
again, the aspect ratio is preserved:

Just as in Scale 4, the Buy/Sell Points
are displayed as green/red arrows on Scale
2. However, on this scale, instead of displaying a
512-day Savitzky-Golay Smoothing Curve, the
2048-day (Robust) Trend Line is displayed. The slope of
this line, denoting the average 2048-day return, is
displayed in the header instead of the slope of the Price
Projection. This is another, probably better, display of
overbought/oversold conditions. In fact, according
to this display, the recent sell-off and
selling climax shows up merely as a correction from a very
overbought condition back to the normal
trend-line. Then the Bollinger Bands are
drawn with respect to this long-term trend-line
instead of the SG Smoothing Curve.

Another feature of this graph is the 200-day Simple
Moving Average (in gray). This is such a popular indicator
that we decided to include it. However, the 200-day MA
is computed with respect to the long-term trend-line,
not some other way. This means that, going to longer and longer term
MAs, they will converge to the long-term trend-line.
Here might be a good place to also point out that you can plot a
wide variety of exponentially weighted moving averages,
in whatever color you want. These are also computed with respect to
the long-term trend-line. For completeness, you can
also plot horizongal lines at any price level, in
any color. (Note: If there are fewer than
2048 days of data, then that number of data days is plotted
on the graph, and the trend line is over that number of days.)

Scale 1 (2019-01-04)

Finally, going down from Scale 2, we reach
Scale 1. This is a panoramic view of the price
action, with one pixel per data day. If your screen is 2048 pixels
wide, you can see the entire price action at once going back 8
years:

This scale has all the same features of Scale 2,
except that there are no Buy/Sell Points shown. But
the 200-day Simple MA is shown on this scale. From
this bird's-eye view it appears that Amazon was
very overbought and the sell-off
and selling climax of the past few months merely
brought it back to its normal trend-line. This kind
of panoramic view is very useful to make such deductions, to avoid
the confusion and hysteria that occurs when everybody is just
looking at the short-term graphs (on a linear scale, without any
perspective).